The proofs of Theorems REF , REF , and REF  (see Sect. ) are based on the theory of inner \(\alpha \) -Riesz balayage as well as on the theory of inner \(\alpha \) -Riesz equilibrium measures, both originated in [1]}, [2]} (see also [3]}–[4]} for some further relevant results). The inner \(\alpha \) -Riesz equilibrium measure is understood in an extended sense where its energy as well as its total mass may be infinite. To make the present study self-contained, we give a brief summary of [1]}–[4]} (see Sects. , ). To begin with, we first review some basic facts of the theory of \(\alpha \) -Riesz potentials, see [7]}.
